Question

A sample of `._(131)^(53) I` is iodide ion was admistered to a patient in a carrier consisting of `0.10 mg` of stable iiodide ion. After 4 day `67.7%` of initial radioactivity was detected in the throid gland of the patient. What mass of stable iodide ion had migrated to thyroid glad? (`t_(1//2)` for iodide ion = 8 day)

Answer 1

If `t = 4`day, `lambda = (0.693)/(8)`, then since `r_(0) prop N_(0)` and `r prop N`
`:. (r_(0))/(r) = (N_(0))/(N)`
`:. t = (2.303)/(lambda) log (r_(0))/(r)`
`4 = (2.303xx8)/(0.693) log (1)/(0.693) log (r_(0))/(r)`
`r = 0.707 r_(0)`
Thus iodide ion left is `0.707` part of intially injected sample, however the rate decreases only `67.7%` or `0.688` in 4 days, thus
If `0.707` is left then iodidie ion migrated to thryorid `=1` Thus `0.677` is left than iodide ion migrated to thyroid
`= (1xx0677)/(0.707) = 0.958` or `95.8%`
of the iodide ion is migrated to gland.